Kappel, Franz; Maksimov, Vyacheslav Robust dynamic input reconstruction for delay systems. (English) Zbl 0963.93043 Int. J. Appl. Math. Comput. Sci. 10, No. 2, 283-307 (2000). The paper deals with the system \[ \begin{aligned} \dot x_1 &=A_1x_1+ CDx_2+ f_1(t),\\ \dot x_2 &=A_2x_2+ f(t, x_1,Dx_2)+ B(t, x_1)u(t),\end{aligned} \]\[ 0\leq t\leq \vartheta,\quad x_1(0)\in X_1,\quad x_2(0)\in X_2, \] a pair of evolutionary equations in Hilbert spaces \(X_1\), \(X_2\) with appropriate definitions of the operators and semigroup generators.The following “inverse” problem is considered: given the “observation” results \(\xi_i\in X_1\), \(i= 1,\dots, m\), find \(u: [0,\vartheta]\to U\) such that \(|x_1(i\delta)- \xi_i|< h\), \(0< h< 1\) where \(x_1(t)\) is the corresponding solution with the given initial condition and \(i\delta\) are the points of a division of the interval \([0,\vartheta]\). Reviewer: Vladimir Răsvan (Craiova) Cited in 3 Documents MSC: 93C23 Control/observation systems governed by functional-differential equations 93C25 Control/observation systems in abstract spaces Keywords:input reconstruction; delay system; inverse problem; evolutionary equations PDFBibTeX XMLCite \textit{F. Kappel} and \textit{V. Maksimov}, Int. J. Appl. Math. Comput. Sci. 10, No. 2, 283--307 (2000; Zbl 0963.93043)